Question

Please for the love of god anwser my question lay correctly I really need your help :( I will give 25 points :)! This is geometry
I need help asap it's rn​

Answer 1

Answer:

$\displaystyle \rm A_{ \text{c - pentagon}} =41$

$\rm \displaystyle P _{ \rm c - pentagon} = 20+ 4 \sqrt{2}$

Step-by-step explanation:

we have a square and a triangle

we want to figure out the area and the perimeter of the pentagon

to figure out the area of the pentagon we can use the given formula:

$\displaystyle \rm A_{ \text{c - pentagon}} = A_{ \text{squre}} - A_{ \text{triangle}}$

let's figure out $A_{\rm square}$:

since the given shape is a square Every angle of its 90° Thus the triangle is a right angle triangle

therefore the height is 4

$\displaystyle A _{ \rm triangle} = \frac{1}{2} \times b \times h$

substitute h and b

$\displaystyle A _{ \rm triangle} = \frac{1}{2} \times 4 \times 4$

reduce fraction:

$\displaystyle A _{ \rm triangle} = 2 \times 4$

simplify multiplication:

$\displaystyle A _{ \rm triangle} = 8$

likewise square

$\displaystyle A _{ \rm squre} = {s}^{2}$

substitute s:

$\displaystyle A _{ \rm squre} = {7}^{2}$

simplify square

$\displaystyle A _{ \rm squre} = 49$

hence,

$\displaystyle \rm A_{ \text{c - pentagon}} =49- 8$

$\displaystyle \rm A_{ \text{c - pentagon}} =41$

to figure out perimeter

let's figure out hypotenuse first

$\displaystyle h = \sqrt{ {4}^{2} + {4}^{2} }$

$\displaystyle h = \sqrt{ 16 + 16}$

$\displaystyle h = 4 \sqrt{2}$

therefore,

$\rm \displaystyle P _{ \rm c - pentagon} = 3 + 3 + 4 \sqrt{2} + 7 + 7$

$\rm \displaystyle P _{ \rm c - pentagon} = 6 + 4 \sqrt{2} + 14$

$\rm \displaystyle P _{ \rm c - pentagon} = 20+ 4 \sqrt{2}$